Simplify: $3((\frac{5}{3})x^2 - 28x + 15) - 5(x^2 + 6x - 15)$
Algebraic Expression Simplification
The goal is to simplify the given algebraic expression:
$3\left(\left(\frac{5}{3}\right)x^2 - 28x + 15\right) - 5(x^2 + 6x - 15)$
Step 1: Distribute the First Constant
Multiply the terms inside the first parenthesis by 3:
- $3 \times \left(\frac{5}{3}\right)x^2 = 5x^2$
- $3 \times (-28x) = -84x$
- $3 \times 15 = 45$
The first part becomes: $5x^2 - 84x + 45$
Step 2: Distribute the Second Constant
Multiply the terms inside the second parenthesis by -5:
- $-5 \times x^2 = -5x^2$
- $-5 \times (6x) = -30x$
- $-5 \times (-15) = 75$
The second part becomes: $-5x^2 - 30x + 75$
Step 3: Combine Like Terms
Combine the results from Step 1 and Step 2:
$(5x^2 - 84x + 45) + (-5x^2 - 30x + 75)$
Group like terms:
- $x^2$ terms: $5x^2 - 5x^2 = 0$
- $x$ terms: $-84x - 30x = -114x$
- Constant terms: $45 + 75 = 120$
The simplified expression is $-114x + 120$.
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Important Questions from Algebric Equations
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
